I drive a (new to me) 2011 Nissan Sentra. The transmission is automatic, and as with most newer cars, it has overdrive.

I'm always wary of wearing my brakes (and particularly the correlation between braking and gas mileage), so I try to avoid hitting them when it's possible. If I see somewhere that I'll need to slow down, I try to coast for long enough that I don't have to touch the brakes.

Failing that, I use engine braking to slow down whenever I can. Here's where I deviate from those questions. First of all, my engine is an automatic, so the answers relating to manual transmissions seem like they might be missing some critical parts. Also, I don't have any large hills I'm braking down, this is almost exclusively before / at a stoplight (so that I barely brake, just slow crawl, then accelerate when it changes).

This gets me down to about 10 mph, and I've never seen the RPMs go anywhere close to red line.

My question is largely about the overdrive scenario, and the long term maintenance repercussions.

First of all, my basic understanding of overdrive is that it's a higher gear (or possibly a set of gears with incremental gear ratios?) that the transmission shifts into when the car is going a good pace (40-45+). With this assumption, I feel that switching it off to engine brake will not damage the transmission, as it's merely downshifting, which is exactly what engine braking is about. Is this correct?

Additionally, is my understanding of engine braking sound as far as the basic gear shifting is concerned (disregarding the overdrive scenario)? My belief is that any wear would be on the opposite side of the contact locations in the transmission (since the wheels are pushing the engine, not the other - usual - way), so any additional "wear" would be unimportant to the overall life of the transmission.

Finally, and I believe this is very important to this discussion: by all accounts (manual, dealership, online), my 2011 Nissan Sentra has a Continuously Variable Transmission. I don't understand transmissions well enough to comprehend the subtle differences, but I do know the CVT has the option of infinite gear ratios, which means it can't possibly be a traditional "gear" transmission. I apologize for dropping this here at the end, but I don't know enough about CVTs to let that guide my questioning.

Am I damaging my transmission by using engine braking heavily in day to day driving?

Not part of the answer below but relevant to "My belief is that...": one of the things that I find most comforting about cars (and most of the physical world, really) is that it doesn't matter what I believe. The car just is. Wear happens. I can find out why. I can fix it.
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Bob Cross♦Sep 21 '12 at 12:08

This gets me down to about 10 mph, and I've never seen the RPMs go
anywhere close to red line.

If this is your procedure, you're well within the engineering tolerances of the design. Your car is not dealing with any kind of excess load. All is well.

With this assumption, I feel that switching it off to engine brake
will not damage the transmission, as it's merely downshifting, which
is exactly what engine braking is about. Is this correct?

Yes, you are correct. This problem clearly illustrates the situation: the overdrive button just allows the transmission to select an even higher gear, primarily for increased mileage at high speeds.

Finally, and I believe this is very important to this discussion: by
all accounts (manual, dealership, online), my 2011 Nissan Sentra has a
Continuously Variable Transmission. I don't understand transmissions
well enough to comprehend the subtle differences, but I do know the
CVT has the option of infinite gear ratios, which means it can't
possibly be a traditional "gear" transmission.

Yes, this does make quite a difference in terms of the design but it doesn't change any of the fundamental answers.

You can see that there are two variable diameter pulleys connected by a very robust belt. As you say, this theoretically allows for an infinite number of gear ratios. Practically, there are plenty of engineering and human interface limitations that reduce infinity to a more manageable set of presets. There is a finite resolution of the pulley adjustment mechanism that allows the engine computer to direct the transmission. This means that, while not quite infinite, you probably have many many more effective gears settings than the five choices I have in my car.

I don't know if this is still relevent with modern computer controlled transmissions. Many,many years ago my transmission rebuilder told me every manual downshift results in one less automatic upshift.
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mikesSep 26 '12 at 21:32

@mikes, I'm trying to understand: do you mean there are a finite amount of shifts for the whole transmission over the life of the car?
–
Bob Cross♦Sep 27 '12 at 0:40

I think what he was trying to imply was, in his opinion it was not a good idea manually downshift an automatic transmission.
–
mikesSep 27 '12 at 0:59

@mikes, in the absence of specific information about a particular situation, I'd have to say that he's wrong: moving the gear selector isn't going to automatically shorten the life of the transmission.
–
Bob Cross♦Sep 27 '12 at 11:40

Perhaps not really an answer, but I always wonder why people would rather put additional wear on an expensive, difficult to repair/replace, non-consumable item (driveline components) rather than on easy to replace consumable items (brake parts).

Well, this is the entire thrust of trying to find out more information. In essence, is making heavy use of engine braking actually removing usable time from the transmission, or is it just balancing where wear happens? That's an actual question. How does heavy engine braking wear the transmission in comparison to rare engine braking and heavy (wheel) brake use?
–
rockerestOct 2 '12 at 20:12